Hierarchical Bayesian modelling for the analysis of the lactation of dairy animals

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English: This thesis was written with the aim of modelling the lactation process in dairy cows and goats by applying a hierarchical Bayesian approach. Information on cofactors that could possibly affect lactation is included in the model through a novel approach using covariates. Posterior distributions of quantities of interest are obtained by means of the Markov chain Monte Carlo methods. Prediction of future lactation cycle(s) is also performed. In chapter one lactation is defined, its characteristics considered, the factors that could possibly influence lactation mentioned, and the reasons for modelling lactation explained. Chapter two provides a historical perspective to lactation models, considers typical lactation curve shapes and curves fitted to the lactation composition traits fat and protein of milk. Attention is also paid to persistency of lactation. Chapter three considers alternative methods of obtaining total yield and producing Standard Lactation Curves (SLAC’s). Attention is paid to methods used in fitting lactation curves and the assumptions about the errors. In chapter four the generalised Bayesian model approach used to simultaneous ly model more than one lactation trait, while also incorporating information on cofactors that could possibly influence lactation, is developed. Special attention is paid not only to the model for complete data, but also how modelling is adjusted to make provision for cases where not all lactation cycles have been observed for all animals, also referred to as incomplete data. The use of the Gibbs sampler and the Metropolis-Hastings algorithm in determining marginal posterior distributions of model parameters and quantities that are functions of such parameters are also discussed. Prediction of future lactation cycles using the model is also considered. In chapter five the Bayesian approach together with the Wood model, applied to 4564 lactation cycles of 1141 Jersey cows, is used to illustrate the approach to modelling and prediction of milk yield, percentage of fat and percentage of protein in milk composition in the case of complete data. The incorporation of cofactor information through the use of the covariate matrix is also considered in greater detail. The results from the Gibbs sampler are evaluated and convergence there-of investigated. Attention is also paid to the expected lactation curve characteristics as defined by Wood, as well as obtaining the expected lactation 254 curve of one of the levels of a cofactor when the influence of the other cofactors on the lactation curve has be eliminated. Chapter six considers the use of the Bayesian approach together with the general exponential and 4-parameter Morant model, as well as an adaptation of a model suggested by Wilmink, in modelling and predicting milk yield, fat content and protein content of milk for the Jersey data. In chapter seven a diagnostic comparison by means of Bayes factors of the results from the four models in the preceding two chapters, when used together with the Bayesian approach, is performed. As a result the adapted form of the Wilmink model fared best of the models considered! Chapter eight illustrates the use of the Bayesian approach, together with the four lactation models considered in this study, to predict the lactation traits for animals similar to, but not contained in the data used to develop the respective models. In chapter nine the Bayesian approach together with the Wood model, applied to 755 lactation cycles of 493 Saanen does collected during either or both of two consecutive year, is used to illustrate the approach to modelling and predicting milk yield, percentage of fat and percentage of protein in milk in the case of incomplete data. Chapter ten provides a summary of the results and a perspective of the contribution of this research to lactation modelling.

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